limn趋于无穷n[e^(a/n)-e^(b/n)]

Question

lim n趋于无穷 n[e^(a/n)-e^(b/n)]

Answer 1

原式=lim(n-->∞)n[e^(b/n)[e^(a-b/n)-1]]
根据x-->0e^x-1~x 上式=lim(n-->∞)n*e^(b/n)*(a-b/n)=a-b